koch曲线与koch雪花的MATLAB实现

代码

% 2016-4-3
function koch(Ax, Ay, Bx, By)
% 控制递归深度
Deepth = 20;
% 控制图画大小
Size = 100;
if ((Bx-Ax)^2 + (By-Ay)^2) < Deepth
   plot([Ax, Bx], [Ay, By], '-r') 
   hold on
   axis([0 Size 0 Size]);
else
    Cx = Ax + (Bx-Ax)/3;
    Cy = Ay + (By-Ay)/3;
    Dx = Bx - (Bx-Ax)/3;
    Dy = By - (By-Ay)/3;
    
    koch(Ax, Ay, Cx, Cy);
    koch(Dx, Dy, Bx, By);
    
    L = sqrt((Dx-Cx)^2 + (Dy-Cy)^2);
    alpha = atan((Dy-Cy)/(Dx-Cx));
    % 数学
    if (alpha>=0 && Dx-Cx<0) || (alpha<0 && (Dx-Cx)<0)
       alpha = alpha + pi;
    end
    
    Ex = Cx + cos(alpha + pi/3)*L;
    Ey = Cy + sin(alpha + pi/3)*L;
    
    koch(Cx, Cy, Ex, Ey);
    koch(Ex, Ey, Dx, Dy);
end
end

% matlab的单步调试有助于理解该递归
% 可通过设置断点观察图形是如何一步一步被画出来的

koch曲线

koch雪花